A Statistical Proof of the Transformation Theorem
Posted: 19 Mar 2012
Date Written: March 17, 2012
Abstract
The well-known transformation theorem (or change-of-variables theorem) is difficult to prove, requiring knowledge of theorems in advanced analysis. For this reason, it is stated without proof in all the statistics textbooks we know of. Here, we provide a new and much simpler proof, by exploiting the fact that it is a density function which is being transformed, and the idea of conditioning.
Suggested Citation: Suggested Citation
Abadir, Karim M. and Magnus, Jan R., A Statistical Proof of the Transformation Theorem (March 17, 2012). Available at SSRN: https://ssrn.com/abstract=2025472
Feedback
Feedback to SSRN
If you need immediate assistance, call 877-SSRNHelp (877 777 6435) in the United States, or +1 212 448 2500 outside of the United States, 8:30AM to 6:00PM U.S. Eastern, Monday - Friday.